Problem: Evaluate the definite integral. $\int^{15}_{5}\big(2x-1\big)\,dx = $
Explanation: First, use the power rule: $\int^{15}_{5}\big(2x-1\big)\,dx ~=~ x^2-x\Bigg|^{{15}}_{5}$ Second, plug in the limits of integration: $\big[{15}^2-{15}\big]-\big[{5}^2-{5}\big] = 210 -20 = 190$. The answer: $\int^{15}_{5}\big(2x-1\big)\,dx ~=~ 190$